Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2014, Article ID 167565, 11 pages http://dx.doi.org/10.1155/2014/167565 Research Article Probabilistic Harmonic Calculation in Distribution Networks with Electric Vehicle Charging Stations Jianxue Wang,1 Yanlin Cui,2 and Minghui Zhu1 1 Department of Electrical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China 2 Power Dispatch and Control Center of Guangdong Power Grid Corporation, Guangzhou, Guangdong 510080, China Correspondence should be addressed to Jianxue Wang; [email protected] Received 25 April 2014; Accepted 28 July 2014; Published 14 August 2014 Academic Editor: Weichao Sun Copyright © 2014 Jianxue Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Integrating EV charging station into power grid will bring impacts on power system, among which the most significant one is the harmonic pollution on distribution networks. Due to the uncertainty of the EV charging process, the harmonic currents brought by EV charging stations have a random nature. This paper proposed a mathematical simulation method for studying the working status of charging stations, which considers influencing factors including random leaving factor, electricity price, and waiting time. Based on the proposed simulation method, the probability distribution of the harmonic currents of EV charging stations is obtained and used in the calculation of the probability harmonic power flow. Then the impacts of EVs and EV charging stations on distribution networks can be analyzed. In the case study, the proposed simulation and analysis method is implemented on the IEEE-34 distribution network. The influences of EV arrival rates, the penetration rate, and the accessing location of EV charging station are also investigated. Results show that this research has good potential in guiding the planning and construction of charging station. 1. Introduction contains the influences induced by uncoordinated charging of large amounts of EVs such as voltage deviations, thermal Car industry has been developing for decades at a cracking overloads, increase in losses, and decrease in voltage stability pace. In order to pursue better performance and higher utility [6, 8–10]. Researches have investigated aspects including the of vehicles, many valuable researches have been done to different EV penetrations on distribution network investment address the issues like adaptive control, mathematical model- [7], the long-term operating capacity reserve [11], and trans- ing, and fault diagnosis [1–3]. In recent years, the pressure of former life [12]. Coordinated charging strategies are proposed fossil fuel shortage and other environmental problems leads [12–15] to promote the distribution gird’s ability to hold more to high-speed development of electric vehicles (EVs) due to EVs without reinforcements, improve voltage profile, and their emission-free characteristic and effective utilization of reduce power losses. renewable energy [4, 5]. The promising trend of EVs attracts The other category is the impacts brought by high rating plenty of researchers to concentrate on the functioning nonlinear switching devices in EV chargers [16]andthe and the influence of electrical vehicles. Unlike conventional typical one in this category is harmonic pollution. Harmonic vehicles, the power supply of EVs mainly comes from local pollution will shorten the life span of transformers, reduce the power distribution system through EV charging stations [6, utilization of transmission lines, and interfere with the signals 7] and that will lead to impacts on distribution network. In of measuring and protection equipment. Therefore, studying order to study the impacts, the EV charging station should the harmonic pollution brought by EV charging stations is of be modeled properly and many factors need to be taken into greatimportance.Paper[17] establishes a stochastic aggregate consideration. harmonic load model to study the harmonic characteristics The impacts of EV charging station integration can be of EV charger. Paper [18] presents a harmonic simulation divided into two categories basically. The first category method to study the harmonic impact of EVs. Paper [19] 2 Journal of Applied Mathematics develops an approach to decrease the harmonics in a high id Rf Lf II EV penetration grid, and the harmonic load flow is used to model the distorted grid and identify the worst bus based on ia thetypicaldailyloadcurve. ua In most of the calculation, the worst situation of har- u u C b d f UI R monic of charging station was used. However, the probability uc of the worst situation is rare in daily life. In most of these studies the harmonic currents are generated by individual EV charger. The random characteristic of charging behavior was not considered in the calculation of charging station Figure 1: The structure diagram of equivalent simplified mode for harmonic and was hardly consistent with the actual situation EV charger [20]. in our daily life. Besides, there are limited studies focused on the system level to evaluate the harmonic distortion of charging stations. 100 In this paper, this problem is investigated from single 90 equipment to the entire system. First, a simplified simulation model of EV charger is used to analyze the harmonic char- 80 acteristics. Second, based on the queuing theory and charger model, a mathematical simulation method to get the proba- 70 bility distribution of charging station state is proposed, con- 60 sidering the influences of random factors, electricity price, and waiting time. The statistics of the simulation results are 50 performed to obtain the probability distribution of total har- monics. Third, through the probability harmonic power flow, 40 the probability characteristics of probability distribution of charging stations’ influences on system harmonics are ana- 30 lyzed. At last, the key factors, including the arrival rate, pen- The efficiency of frequencyhigh converter DC/DC 20 etration rate, and the access location of EV charging station, 0 1 2 3 4 5 6 7 8 9 were analyzed based on a modified IEEE-34 system. Output power (kW) Figure 2: The relationship between efficiency and output power. 2. The Working State Model of EV Charging Station the output voltage of three-phase uncontrolled rectifier, and 2.1. Model the EV Charger. In order to analyze the harmonic is the output current of three-phase uncontrolled rectifier. characteristic of EV charging station, the basic working According to (1), the equivalent resistance should be a modelofasingleEVchargerneedstobebuiltfirst.Inthis function of the charging time to reflect the different output paper, we consider a kind of currently the most widely used power in different charging stages. The empirical formula of EV charger. This typical EV charger consists of a three-phase during the charging process was obtained through fitting uncontrolledrectifierandahighfrequencyDC/DCconverter the actual-measured data [20], which can be put as which are coupled with a high frequency transformer [4]. The outputvoltageandcurrentofthechargerarecontrolledby 0.048 {0.79max , 0<<, feedback control equipment in the high frequency DC/DC () = { −0.021(−) (2) converter. Since elaborately modeling the EV charger is too {max ,<<max, complicated, it consumes much time for the simulation. To reduce the complexity of the EV charger model, a sim- where is the output power of EV charger, is charging plification proposed in20 [ ] is adopted here, where the high time, isthetimespotwhenchargingmodeturnsfrom frequency DC/DC converter and battery load are replaced by constantcurrentchargingtoconstantvoltagecharging,max an equivalent resistance. The simplified equivalent circuit is is the maximum charging time, and max is the rated output shown in Figure 1. power. BasedonOhm’slaw,theequivalentresistancecanbe In [20], was treated as a constant; however, according calculated as to the simulation result in MATLAB/Simulink environment, 2 2 the efficiency of the high frequency DC/DC converter () = = = , (1) varies with the output power of the EV charger .Their () () () relationship is presented in Figure 2. Using the curve-fitting technique, the expression can be where is the equivalent resistance of high frequency obtained as DC/DC converter, is the input power of the high frequency −0.011 + 193 DC/DC converter, is the output power of EV charger, ( ) = . 2 (3) is the efficiency of high frequency DC/DC converter, is 1 + 1.785 + 0.012 Journal of Applied Mathematics 3 Through1 ( )–(3), we can get the value of equivalent resis- Arrive Finish and tance at any time spot during charging. EV cars need Waiting in Charging leave charging line To illustrate the effectiveness of the simplified model in harmonic analysis, a comparison between the original and Figure 3: The diagram of EVs’ charging process. the simplified model (considering the varying efficiency dur- ing charging) has been made through simulating in MAT- LAB/Simulink environment. Simulation results show that the q maximum error of the harmonic between the original and q the simplified model is merely 0.45%, while the equivalent q simplified model costs 40% less time than the original one. ··· p p Therefore, the simplified model appears to be more effec- 10 20 30 60 80 100 tive and suitable, especially when